# ch70 - CHAPTER 7: FLOW PAST IMMERSED BODIES *(unbounded...

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CHAPTER 7: FLOW PAST IMMERSED BODIES *(unbounded flows)

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Ch 7: FLOW PAST IMMERSED BODIES FLAT PLATE (CAN’T HAVE FULLY DEVELOPED FLOW) What is wrong with this picture?
BLUNT OBJECT Ch 7: FLOW PAST IMMERSED BODIES (CAN’T HAVE FULLY DEVELOPED FLOW)

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Paradoxes Pipe Flow - hydraulic engineers knew Δ p ~ U avg 2 - theory and capillary tube showed Δ p ~ U avg - several other paradoxes for external flows as well Drag - theory predict no drag (1744 –d’Alembert)
Shape and Flow – Irvin Shapiro http://web.mit.edu/fluids/www/Shapiro/ncfmf.html Fluid Dynamics of drag Parts I - IV

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Air speeds up to 230 mph, drag forces object in jet upwards, causing spring to extend downwards Pressurized settling chamber underneath desk EXPERIMENTAL SET UP
Tubing leads air from settling chamber to U-tube manometer which is calibrated in mph, so can measure drag force and speed. Can measure U and Drag

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Question #1: sketch the graph of drag on smooth 3” diameter sphere vs velocity PARADOX #1 SPHERE 0 250 MPH 125 MPH
D ~ U 2 D ~ U D = 6 πμ RU Drag lower at higher speed! 250 mph 125 mph SPHERE

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D ~ U 2 D ~ U D = 6 πμ RU ASIDE: viscous drag at low Re number does not depend on density or pressure. SPHERE ASIDE
“The new law that he {Maxwell ~1862} predicted seemed to defy common sense. It was that the viscosity of a gas – the internal friction that causes drag on a body that moves through it – is independent of pressure. One might expect that a more compressed gas to exert a greater drag.” The Man Who Changed Everything – Basil Mahon Turns out that the effect of being surrounded by more molecules is exactly cancelled out by the fact that their mean free path is less.

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When very small dust particles fall through one column of air at 1 atmospheric, they fall at the same terminal velocity as if it was 0.01 atmosphere.
is roughened, what happens to drag? PARADOX #2

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## This note was uploaded on 04/26/2010 for the course MAE 101B 101B taught by Professor Rohr during the Summer '09 term at UCSD.

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ch70 - CHAPTER 7: FLOW PAST IMMERSED BODIES *(unbounded...

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